A. Athermalization
As known in the art, the optical properties of an optical system normally vary with changes in temperature as a result of: (i) changes in the indices of refraction of the optical materials used in the system, (ii) changes in the shape of the optical elements used in the system, (iii) changes in the dimensions of the housing used to hold the optical elements, and (iv) changes in the wavelength or frequency of the light source employed in the system.
Such changes in optical properties with changes in temperature are undesirable and extensive efforts have been made to solve this problem, examples of which can be found in the following patents and literature references: Londono et al., U.S. Pat. No. 5,260,828; Borchard, U.S. Pat. No. 5,504,628; Behrmann et al., "Influence of temperature on diffractive lens performance," Appl. Opt., 1993, 32: 2483-2489; D. S. Grey, "Athermalization of Optical Systems," JOSA, 1948, 38:542-546; T. H. Jamieson, "Thermal effects in optical systems," Opt. Eng., 1981, 20:156-160; Kryszcynski et al., "Material problem in athermalization of optical systems," Opt. Ens., 1997, 36:1596-1601; Londono et al., "Athermalization of a single-component lens with diffractive optics," Appl. Opt., 1993, 32:2295-2302; Tamagawa et al., "Dual-band optical systems with a projective athermal chart: design," Appl. Opt., 1997, 36:297-301; and Handbook of Optics, 2nd ed., M. Bass editor, McGraw-Hill, Inc., New York, 1995, volume I, 32.15-32.16.
The thermal behavior of an optical surface can be described in terms of the surface's "optothermal" coefficient defined as: ##EQU1##
where ".PHI." is optical power and "T" is temperature.
For a refractive surface separating a first medium having an index of refraction n.sub.1 and a second medium having an index of refraction n.sub.2, X.sub..PHI.,R is given by: ##EQU2##
where .alpha. is the coefficient of thermal expansion of the substrate medium (i.e., the solid medium which forms the refractive surface) and where the paraxial optical power of the surface, .PHI..sub.R, is given by: ##EQU3##
where R.sub.0 is the vertex radius of the refractive surface.
The corresponding expression for a diffractive kinoform surface is: EQU X.sub..PHI.,K =-2.alpha. (III)
where again .alpha. is the coefficient of thermal expansion of the substrate medium (in this case, the solid medium which forms the kinoform surface) and where the paraxial optical power of the surface, .PHI..sub.K, is given by: ##EQU4##
where D.sub.0 is the clear aperture diameter of the kinoform surface, N is the total number of zones within the clear aperture, and .lambda..sub.0 is the system's nominal operating wavelength.
Table 1 sets forth values of X.sub..PHI.,R and X.sub..PHI.,K for various optical materials which can be used in the visible, infra-red (IR), or ultra-violet (UV) regions of the spectrum, as well as ratios of X.sub..PHI.,K to X.sub..PHI.,R for these materials. For Si and Ge, the fact that the optothermal coefficients for kinoforms are much smaller than those for refractive components can make it difficult to athermalize a refractive system composed of these materials with a kinoform. For these as well as the other materials in this table, the use of a kinoform can complicate the athermalization process since unlike stepped diffractive surfaces (see below), kinoforms introduce optical power into the system at the system's nominal operating wavelength (.lambda..sub.0).
B. Stepped Diffractive Surfaces
FIGS. 1A and 1B illustrate optical elements employing stepped diffractive surfaces 13a and 13b of the type with which the present invention is concerned. To simplify these drawings, opposing surfaces 15a and 15b of these elements have been shown as planar. In the general case, the opposing surfaces can have optical power or can be another stepped diffractive surface, if desired.
As shown in these figures, stepped diffractive surfaces 13 comprise a plurality of concentric planar zones 17 (also referred to as "steps") which are orthogonal to optical axis 19. The zones lie on a base curve which is shown as part of a circle in FIGS. 1A and 1B, but in the general case can be any curve of the type used in optical design, including conics, polynomial aspheres, etc. The base curve may also constitute a base surface in cases where the concentric planer zones are not axially symmetric, i.e., where their widths are a function of .theta. in an (r, .theta., z) cylindrical coordinate system having its z-axis located along the system's optical axis. For ease of reference, the phrase "base curve" will be used herein and in the claims to include both the axially symmetric and axially non-symmetric cases, it being understood that in the non-symmetric case, the base curve is, in fact, a base surface. In either case, the base curve can be characterized by a vertex radius Ro which, as discussed below, can be used in calculating the paraxial properties of the stepped diffractive surface.
The stepped diffractive surfaces of the invention are distinguished from digitized (binary) kinoforms by the fact that the sag of the stepped diffractive surface changes monotonically as the zone number increases. The sag of the surface of a binary kinoform, on the other hand, always exhibits a reversal in direction at some, and usually at many, locations on the surface. This is so even if the base curve for the binary kinoform has a monotonic sag.
Quantitatively, the zones of the stepped diffractive surface preferably have widths (w.sub.i) and depths (d.sub.i) which satisfy some or all of the following relationships: EQU .vertline.d.sub.i.vertline..backslash..vertline.d.sub.i+1.vertline.&lt;2.0, for i=1 to N-2; EQU .vertline.d.sub.i.vertline..ident.j.sub.i.lambda..sub.0 /.vertline.(n.sub.2 -n.sub.1).vertline., for i=1 to N-1;
and EQU w.sub.i /.lambda..sub.0 &gt;1.0, for i=1 to N;
where "j.sub.i " is the order of the ith zone of the stepped diffractive surface (j.sub.i &gt;1), N is the total number of zones (N=6 in FIGS. 1A and 1B), and "n.sub.1 " and "n.sub.2 " are the indices of refraction of the media on either side of the stepped diffractive surface, with light traveling through the stepped diffractive surface from the n.sub.1 medium to the n.sub.2 medium.
The "j.sub.i " nomenclature is used in the above equations to indicate that the working order of the stepped diffractive surface can be different for different zones. In many cases, the same working order will be used for all zones; however, for manufacturing reasons, it may be desirable to use different working orders for some zones, e.g., if the zone width wi would become too small for accurate replication with a constant working order, especially, for a constant working order of 1. In this regard, it should be noted that j.sub.i can be made greater than 1 for all zones, again to facilitate manufacture of the stepped diffractive surface by, for example, reducing the overall number of zones comprising the surface and, at the same time, increasing the depth and width of the individual steps.
Like the monotonic sag characteristic, the .vertline.d.sub.i.vertline..backslash..vertline.d.sub.i+1.vertline.&lt;2.0 characteristic distinguishes the diffractive surfaces of the invention from digitized (binary) kinoforms, where .vertline.d.sub.i.vertline..backslash..vertline.d.sub.i+1.vertline. is normally greater than 2.0 for at least some steps, i.e., where the kinoform profile returns to the base curve. The .vertline.d.sub.i.vertline..ident.j.sub.i.lambda..sub.0 /.vertline.(n.sub.2 -n.sub.1).vertline. characteristic in combination with the requirement that j.sub.i.gtoreq.1 also distinguish the stepped diffractive surfaces of the invention from digitized kinoforms in that this expression calls for an optical path difference for each step of at least j.sub.i.lambda..sub.0 while for a digitized kinoform of the same diffractive order the optical path difference for each step is at most j.sub.i.lambda..sub.0 /2 in the case of a two level digitization and becomes even smaller for the digitizations actually used in practice, e.g., an eight or sixteen level digitization. The w.sub.i /.lambda..sub.0 &gt;1.0 characteristic affects the efficiency of the stepped diffractive surface, with larger ratios generally corresponding to greater efficiencies. See G. J. Swanson, Binary Optics Technology: Theoretical Limits on the Diffraction Efficiency of Multilevel Diffractive Optical Elements, Massachusetts Institute of Technology Lincoln Laboratory Technical Report 914, Mar. 1, 1991, p.24.
It should be noted that when a stepped diffractive surface is incorporated in an optical element as illustrated in FIGS. 1A and 1B, the optical material making up the element can have an index of refraction greater than or less than the surrounding medium. Also, light can pass from left to right or from right to left through the element. Thus, for a stepped diffractive surface which transmits light, four cases are possible: 1) passage from a higher index of refraction medium to a lower index of refraction medium through a concave stepped diffractive surface; 2) passage from a lower index of refraction medium to a higher index of refraction medium through a concave stepped diffractive surface; 3) passage from a higher index of refraction medium to a lower index of refraction medium through a convex stepped diffractive surface; and 4) passage from a lower index of refraction medium to a higher index of refraction medium through a convex stepped diffractive surface. As further variations, rather than transmitting light, the stepped diffractive surface 13 can be reflective. Combinations of these various cases can, of course, be used in optical systems which employ the invention.
C. Prior Disclosures of Stepped Diffractive Surfaces
The earliest reference discussing the use of a stepped diffractive surface in an optical system is A. I. Tudorovskii, "An Objective with a Phase Plate," Optics and Spectroscopy, Vol. 6(2), pp. 126-133 (February 1959). The optical system considered by Tudorovskii was a telescope objective and the stepped diffractive surface was designed to correct the system's secondary color. Significantly, with regard to the present invention, the Tudorovskii article does not provide any disclosure regarding athermalizing an optical system with a stepped diffractive surface.
U.S. Pat. No. 5,153,778, which issued to Jose M. Sasian-Alvarado in 1992, also discloses a stepped diffractive surface. The Sasian-Alvarado system is monochromatic and the stepped diffractive surface is said to be useful for correcting field curvature and/or spherical aberration. With regard to the present invention, this patent does not mention employing a stepped diffractive surface to achieve athermalization.
In 1993, Jose M. Sasian-Alvarado and Russell A. Chipman published an article on stepped diffractive surfaces entitled "Staircase lens: a binary and diffractive field curvature corrector," Applied Optics, Vol. 32, No. 1, Jan. 1, 1993, pages 60-66. Again, no mention of athermalization was made in connection with this discussion of stepped diffractive surfaces.
Finally, U.S. Pat. No. 5,629,799, which issued to Maruyama et al. in 1997, discloses the use of stepped diffractive surfaces to correct chromatic aberrations in optical disc readers. Once again, the use of a stepped diffractive surface to achieve athermalization is not mentioned.
In addition to not disclosing the use of stepped diffractive surfaces to achieve athermalization, none of the above prior disclosures provides a ray tracing technique which explicitly specifies the spacing and blaze angle of the steps of an SDS. Among other things, the lack of such a ray tracing technique means that these references cannot account for the actual physical changes to the microstructure of the surface which occur as a result of a change in temperature.